Rafał Wcisło

A 3-D model of tumor progression based on complex automata driven by particle dynamics.

The dynamics of a growing tumor involving mechanical remodeling of healthy tissue and vasculature is neglected in most of the existing tumor models. This is due to the lack of efficient computational framework allowing for simulation of mechanical interactions. Meanwhile, just these interactions trigger critical changes in tumor growth dynamics and are responsible for its volumetric and directional progression. We describe here a novel 3-D model of tumor growth, which combines particle dynamics with cellular automata concept. The particles represent both tissue cells and fragments of the vascular network. They interact with their closest neighbors via semi-harmonic central forces simulating mechanical resistance of the cell walls. The particle dynamics is governed by both the Newtonian laws of motion and the cellular automata rules. These rules can represent cell life-cycle and other biological interactions involving smaller spatio-temporal scales. We show that our complex automata, particle based model can reproduce realistic 3-D dynamics of the entire system consisting of the tumor, normal tissue cells, blood vessels and blood flow. It can explain phenomena such as the inward cell motion in avascular tumor, stabilization of tumor growth by the external pressure, tumor vascularization due to the process of angiogenesis, trapping of healthy cells by invading tumor, and influence of external (boundary) conditions on the direction of tumor progression. We conclude that the particle model can serve as a general framework for designing advanced multiscale models of tumor dynamics and it is very competitive to the modeling approaches presented before.

Macro-Scale Simulations Using Molecular Dynamics Method

Abstract In this paper a new approach to the simulation of shock phenomena is presented. The discrete model of matter description is applied. The system representing a physical object consists of a large number of mutually interacting “particles” (N ∼ 105 +). The model can be used as an alternative to the model of continuous medium described by the sets of partial differential equations solved numerically, using for example the finite elements method. For the presented method, the time evolution of the particle system is described by the Newtonian laws of motion. Application of this approach for simulation of stress and shock phenomena is discussed. The results of selected simulations of the penetration mechanics, explosion and squashing are presented.

PAM: Particle Automata in Modeling of Multiscale Biological Systems

Serious problems with bridging multiple scales in the scope of a single numerical model make computer simulations too demanding computationally and highly unreliable. We present a new concept of modeling framework that integrates the particle method with graph dynamical systems, called the particle automata model (PAM). We assume that the mechanical response of a macroscopic system on internal or external stimuli can be simulated by the spatiotemporal dynamics of a graph of interacting particles representing fine-grained components of biological tissue, such as cells, cell clusters, or microtissue fragments. Meanwhile, the dynamics of microscopic processes can be represented by evolution of internal particle states represented by vectors of finite-state automata. To demonstrate the broad scope of application of PAM, we present three models of very different biological phenomena: blood clotting, tumor proliferation, and fungal wheat infection. We conclude that the generic and flexible modeling framework provided by PAM may contribute to more intuitive and faster development of computational models of complex multiscale biological processes.

Particle Based Model of Tumor Progression Stimulated by the Process of Angiogenesis

We discuss a novel metaphor of tumor progression stimulated by the process of angiogenesis. The realistic 3-D dynamics of the entire system consisting of the tumor, tissue cells, blood vessels and blood flow can be reproduced by using interacting particles. The particles mimic the clusters of tumor cells. They interact with their closest neighbors via semi-harmonic forces simulating mechanical resistance of the cell walls and the external pressure. The particle dynamics is governed by both the Newtonian laws of motion and the rules of cell life-cycle. The particles replicate by a simple mechanism of division, similar to that of a single cell reproduction and die due to necrosis or apoptosis. We conclude that this concept can serve as a general framework for designing advanced multi-scale models of tumor dynamics. In respect to spatio-temporal scale, the interactions between particles can define e.g., cluster-to-cluster, cell-to-cell, red blood cells and fluid particles interactions, cytokines motion, etc. Consequently, they influence the macroscopic dynamics of the particle ensembles in various sub-scales ranging from diffusion of cytokines, blood flow up to growth of tumor and vascular network expansion.

Interactive Visualization Tool for Planning Cancer Treatment

We discuss the components and main requirements of the interactive visualization and simulation system intended for better understanding the dynamics of solid tumor proliferation. The heterogeneous Complex Automata, discrete-continuum model is used as the simulation engine. It combines Cellular Automata paradigm, particle dynamics and continuum approaches to model mechanical interactions of tumor with the rest of tissue. We show that to provide interactivity, the system has to be efficiently implemented on workstations with multiple cores CPUs controlled by OpenMP interface and/or empowered by GPGPU accelerators. Currently, the computational power of modern CPU and GPU processors enable to simulate the tumors of a few millimeters in diameter in its both avascular and angiogenic phases. To validate the results of simulation with real tumors, we plan to integrate the tumor modeling simulator with the Graph Investigator tool. Then one can validate the simulation results on the base of topological similarity between the tumor vascular networks obtained from its direct observation and simulation. The interactive visualization system can have both educational and research aspects. It can be used as a tool for clinicians and oncologists for educational purposes and, in the nearest future, in medical in silico labs doing research in anticancer drug design and/or in planning cancer treatment.

GPU enhanced simulation of angiogenesis

In the paper we present the use of graphic processor units to accelerate the most time-consuming stages of a simulation of angiogenesis and tumor growth. By the use of advanced CUDA mechanisms such as shared memory, textures and atomic operations, we managed to speed up the CUDA kernels by a factor of 57x. However, in our simulation we used the GPU as a co-processor and data from CPU was copied back and forth in each phase. It decreased the speedup of rewritten stages by 40%. We showed that the performance of the entire simulation can be improved by a factor of 10 up to 20.

Particle model of tumor growth and its parallel implementation

We present a concept of a parallel implementation of a novel 3-D model of tumor growth. The model is based on particle dynamics, which are building blocks of normal, cancerous and vascular tissues. The dynamics of the system is driven also by the processes in microscopic scales (e.g. cell life-cycle), diffusive substances - nutrients and TAF (tumor angiogenic factors) - and blood flow. We show that the cell life-cycle (particle production and annihilation), the existence of elongated particles, the influence of continuum fields and blood flow in capillaries, makes the model very tough for parallelization in comparison to standard MD codes. We present preliminary timings of our parallel implementation and we discuss the perspectives of our approach.

A Metaphor of Complex Automata in Modeling Biological Phenomena

We demonstrate that Complex automata (CxA) - a hybrid of a Particle method (PM) and Cellular automata (CA) — can serve as a convenient modeling framework in developing advanced models of biological systems. As a proof_of_concept we use two processes of pathogenic growth: cancer proliferation and Fusarium graminearum wheat infection. The ability of mimicking both mechanical interactions of tumor with the rest of tissue and penetration properties of F.graminearum, confirms that our model can reproduce realistic 3-D dynamics of complex biological phenomena. We discuss the scope of application of CxA in the context of its implementation in CUDA GPU environment.

Continuous and Discrete Models of Melanoma Progression Simulated in Multi-GPU Environment

Existing computational models of cancer evolution mostly represent very general approaches for studying tumor dynamics in a homogeneous tissue. Here we present two very different cancer models: the heterogeneous continuous/discrete and purely discrete one, focusing on a specific cancer type – melanoma. This tumor proliferates in a complicated heterogeneous environment of the human skin. The results from simulations obtained for the two models are confronted in the context of their possible integration into a single multi-scale system. We demonstrate that the interaction between the tissue – represented by both the concentration fields (the continuous model) and the particles (the discrete model) – and the discrete network of blood vessels is the crucial component, which can increase the simulation time even one order of magnitude. To compensate this time lag, we developed GPU/CUDA implementations of the two melanoma models. Herein, we demonstrate that the continuous/discrete model, run on a multi-GPU cluster, almost fifteen times outperforms its multi-threaded CPU implementation.

PAM: Particle automata model in simulation of Fusarium graminearum pathogen expansion.

The multi-scale nature and inherent complexity of biological systems are a great challenge for computer modeling and classical modeling paradigms. We present a novel particle automata modeling metaphor in the context of developing a 3D model of Fusarium graminearum infection in wheat. The system consisting of the host plant and Fusarium pathogen cells can be represented by an ensemble of discrete particles defined by a set of attributes. The cells-particles can interact with each other mimicking mechanical resistance of the cell walls and cell coalescence. The particles can move, while some of their attributes can be changed according to prescribed rules. The rules can represent cellular scales of a complex system, while the integrated particle automata model (PAM) simulates its overall multi-scale behavior. We show that due to the ability of mimicking mechanical interactions of Fusarium tip cells with the host tissue, the model is able to simulate realistic penetration properties of the colonization process reproducing both vertical and lateral Fusarium invasion scenarios. The comparison of simulation results with micrographs from laboratory experiments shows encouraging qualitative agreement between the two.